one pulley may be resolved, so far as the direction of the pull is concerned, into two or more units or single-joint muscles (Fig. 362). The tendons of the Flexor profundus digitorum, for example, pass through several pulleys formed by fibrous sheaths. The direction of the pull is different for each joint and varies for each joint according to the position of the bones. The direction is determined in each case, however, by a straight line between the centers of the pulleys on either side of the joint (Fig. 363). The direction of the pull in any of the segments would not be altered by any change in the position or origin of the muscle belly above the proximal pulley.

The Action of the Muscle Pull on the Tendon.Where the muscle fibers are parallel or nearly parallel to the direction of the tendon the entire strength of the muscle contraction acts in the direction of the tendon.

In pinnate muscles, however, only a portion of the strength of contraction is efficient in the direction of the tendon, since a portion of the pull would tend to draw the tendon to one side, this is mostly annulled by pressure of surrounding parts. In bipinnate muscles this lateral pull is counterbalanced. If, for example, the muscle fibers are inserted into the tendon at an angle of 60 degrees (Fig. 364), it is easy to determine by the parallelogram of forces that the strength of the pull along the direction of the tendon is equal to one-half the muscle pull.

T = tendon, m = strength and direction of muscle pull.

t = component acting in the direction of the tendon.

φ = angle of insertion of muscle fibers into tendon.

cos φ = t/m cos &angle; 60° = 0.50000

0.5 = t/mt = 1/2 m

If

< φ = 72° 30'

cos = 1/3

< φ = 41° 20'

cos = 3/4

< φ = 90°

cos = 0

< φ = 0°

cos = 1

The more acute the angle φ, that is the smaller the angle, the greater the component acting in the direction of the tendon pull. At 41° 20 three-fourths of the pull would be exerted in the direction of the tendon and at 0° the entire strength. On the other hand, the greater the angle the smaller the tendon component; at 72° 30 one-third the muscle strength would act in the direction of the tendon and at 90° the tendon component would be nil.

The Strength of Muscles.The strength of a muscle depends upon the number of fibers in what is known as the physiological cross-section, that is, a section which passes through practically all of the fibers. In a muscle with parallel or nearly parallel fibers which have the same direction as the tendon this corresponds to the anatomical cross-section, but in unipinnate and bipinnate muscles the physiological cross-section may be nearly at right angles to the anatomical cross-section as shown in Fig. 365. Since Huber has shown that muscle fibers in a single fasciculus of a given muscle vary greatly in length, in some fasciculi from 9 mm. to 30.4 mm., it is unlikely that the physiological cross-section will pass through all the fibers. Estimates have been made of the strength of muscles and it is probable that coarse-fibered muscles are somewhat stronger per square centimeter of physiological